Theorem 3bitr4ri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 2-Sep-1995)

	Ref	Expression
Hypotheses	3bitr4i.1	$$⊢\phi \leftrightarrow \psi$$
	3bitr4i.2	$$⊢\chi \leftrightarrow \phi$$
	3bitr4i.3	$$⊢\theta \leftrightarrow \psi$$
Assertion	3bitr4ri	$$⊢\theta \leftrightarrow \chi$$

Proof

Step	Hyp	Ref	Expression
1		3bitr4i.1	$$⊢\phi \leftrightarrow \psi$$
2		3bitr4i.2	$$⊢\chi \leftrightarrow \phi$$
3		3bitr4i.3	$$⊢\theta \leftrightarrow \psi$$
4	1 3	bitr4i	$$⊢\phi \leftrightarrow \theta$$
5	2 4	bitr2i	$$⊢\theta \leftrightarrow \chi$$